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Mixing solid copper, $5\%$ vinegar, and hydrogen peroxide ($\ce{H2O2}$) causes copper acetate to form. The process will occur very slowly without hydrogen peroxide. Adding $\ce{H2O2}$ speeds the formation of copper acetate.

How can I test the solution to see if all of the acetic acid has been converted into copper acetate?

If possible, provide answers that employ only household items or readily available devices.

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Your question and title do not correspond, IMHO. I'll answer one of both:

Vinegar is mostly water, with some acetic acid ($5\%$). A classic experiment, performed by a lot of kids at school, is to mix vinegar with baking soda. The baking soda neutralizes the acid and produces carbon dioxide. The carbon dioxide is what you're looking for: it's the sign that the reaction is taking place.

Pour a pinch of baking soda inside your solution. If it makes bubbles on contact, your solution still contains a lot of vinegar. If you don't see any bubbles, even when stirring, most of the acid has been consumed.

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